1. Field of the Invention
The present invention relates to a method of generating a display of a surface. It is particularly, but not exclusively, concerned with such a method as applied to the generation of curved or shaped surfaces in computer-aided design (CAD) and and/or computed-aided manufacturing (CAM). The present invention also relates to an apparatus for generating a display of a surface.
2. Summary of the Prior Art
It is now common for CAD/CAM systems to be used to design objects such as furniture, automobiles etc., using computers.
The first stage in the design of an object involves the generation of a skeleton of that object, which skeleton comprises shape characteristic lines defining an outline of the object to be generated. The resulting structure is known as a wireframe. Normally, additional lines are then added to the wireframe so that the lines define a multiplicity of adjacent quadrilaterals in a three-dimensional space. Next, curved surfaces are generated to define the shape of the surface within each of the quadrilaterals, which curve surfaces are known as quadrilateral patches.
When the quadrilateral patches are generated, they must adjoin so that the connection therebetween is smooth, so that the object will have a smooth surface. When each quadrilateral patch is generated, points on the patch are represented by vector functions, and there is a smooth transition of the vector functions over the quadrilateral patch. The vector functions normally used are Bezier or B-spline bi-cubic expressions with two parameters, because use of those expressions makes the resulting calculations relatively straightforward.
Generally, known methods have been limited to the use of quadrilateral patches. It has been found, however, that complex processing is needed to achieve a smooth connection between adjacent patches. Furthermore, if the whole of the surface has to be expressed by quadrilaterals, it is sometimes difficult to represent accurately the surface of the object desired. Thus, it is desirable to permit an arbitrary shape to be represented more easily.
In order to reduce the latter problem, JP-A-63-159982 proposed that trilateral patches be used in addition to quadrilateral patches. Use of both trilateral and quadrilateral patches sometimes make it easier to define the surface of the object. However, it was then still necessary to ensure that the trilateral and quadrilateral patches were connected together smoothly.
To address the problem of connecting the patches together smoothly, JP-A-3-68098 proposed that the gradients on both sides of a line representing the join of adjacent patches be the same, so as to impose a surface continuity condition on the patch surfaces. However, if an excessive amount of processing was to be avoided, it was necessary to limit the number of points along the line joining the two surfaces for which gradients were assessed. Alternatively, in JP-A-3-228181, a imaginary ball of a suitable radius was rolled so that it maintained contact with the two adjacent surfaces along the line, of join. The shape of the join was then modified to correspond to the locus of the surface of the ball between the contact points of the ball and the surfaces.